gustavogrds gustavogrds - 1 year ago 419
Python Question

Calculate curl of a vector field in Python and plot it with matplotlib

I need to calculate the curl of a vector field and plot it with matplotlib. A simple example of what I am looking for could be be put like that:

How can I calculate and plot the curl of the vector field in the in the matplotlib gallery?

Please let me know if I can be more specific than that.

Answer Source

You can use sympy.curl() to calculate the curl of a vector field.


Suppose you have:
F = (y2z,-xy,z2) = y2zx - xyy + z2z, then y would be R[1], x is R[0] and z is R[2] while the vectors of the 3 axes would be R.x, R.y, R.z and the code to calculate the vector field curl is:

from sympy.physics.vector import ReferenceFrame
from sympy.physics.vector import curl
R = ReferenceFrame('R')

F = R[1]**2 * R[2] * R.x - R[0]*R[1] * R.y + R[2]**2 * R.z

G = curl(F, R)  

In that case G would be equal to R_y**2*R.y + (-2*R_y*R_z - R_y)*R.z or, in other words,
G = (0, y2, -2yz-y).

To plot it you need to convert the above result into 3 separate functions; u,v,w.

(example below adapted from the matplotlib example on this link):

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.gca(projection='3d')

x, y, z = np.meshgrid(np.arange(-0.8, 1, 0.2),
                      np.arange(-0.8, 1, 0.2),
                      np.arange(-0.8, 1, 0.8))

u = 0
v = y**2
w = -2*y*z - y

ax.quiver(x, y, z, u, v, w, length=0.1)

And the final result is this:

enter image description here

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